Problem: $\dfrac{ -3j + 5k }{ 10 } = \dfrac{ 6j + 9l }{ 10 }$ Solve for $j$.
Explanation: Notice that the left- and right- denominators are the same $\dfrac{ -3j + 5k }{ {10} } = \dfrac{ 6j + 9l }{ {10} }$ So we can multiply both sides by $10$ ${10} \cdot \dfrac{ -3j + 5k }{ {10} } = {10} \cdot \dfrac{ 6j + 9l }{ {10} }$ $-3j + 5k = 6j + 9l $ Combine $j$ terms on the left. $-{3j} + 5k = {6j} + 9l$ $-{9j} + 5k = 9l$ Move the $k$ term to the right. $-9j + {5k} = 9l$ $-9j = 9l - {5k}$ Isolate $j$ by dividing both sides by its coefficient. $-{9}j = 9l - 5k$ $j = \dfrac{ 9l - 5k }{ -{9} }$ Swap signs so the denominator isn't negative. $j = \dfrac{ -{9}l + {5}k }{ {9} }$